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Q.

All x satisfying ${(\cot^{- 1} x)}^{2} - 7 (\cot^{- 1} x) + 10 > 0$ lie in the interval

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a

$(\cot 2, \infty)$

b

$(- \infty, \cot 5) \cup (\cot 4, \cot 2)$

c

$(\infty, \cot 5) \cup (\cot 2, \infty)$

d

$(\cot 5, \cot 4)$

answer is A.

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Detailed Solution

$(\cot^{- 1} x - 5) (\cot^{- 1} x - 2) > U$

Question Image

$\cot^{- 1} x \in (- \infty, 2) \cup (5, \infty) x \in (- \infty, \cot 5) \cup (\cot 2, \infty)$

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All x satisfying cot-1x2-7cot-1x+10>0 lie in the interval